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  "body": "\n## Summary\n\nDodgson condensation is a method to compute the [[determinant|00KDZRW4C0]] of a square matrix by repeatedly replacing it with a smaller matrix of connected $2 \\times 2$ minors.\nEach step divides by interior entries of the matrix from two steps before.\nIt rests on the Desnanot–Jacobi identity, a case of [[Sylvester's determinant identity|7SSKBQYFW1]].\nIt was proposed by Charles Dodgson, better known as Lewis Carroll.\n\n## Explanations\n\n### L1 human\n\nStart with an $n \\times n$ matrix and replace each $2 \\times 2$ block of neighbouring entries by its determinant.\nThis gives an $(n-1) \\times (n-1)$ matrix.\nRepeat, but now divide each new entry by the matching inner entry of the matrix two steps back.\nAfter $n - 1$ steps a single number is left, and it is the determinant.\nFor $A = \\begin{pmatrix} 1 \u0026 2 \u0026 3 \\\\ 4 \u0026 5 \u0026 6 \\\\ 7 \u0026 8 \u0026 10 \\end{pmatrix}$, the first step gives $\\begin{pmatrix} -3 \u0026 -3 \\\\ -3 \u0026 2 \\end{pmatrix}$, and the second gives $(-6 - 9)/5 = -3 = \\det A$.\n",
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